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Seminar 2: Decomposition analysis and its utility in Agricultural Economics research.

Student: ADITYA K.S., PALB (1094)

Major Advisor: Dr. T.N. Prakash Kammardi

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ROAD MAP……Sl. No Particulars

1 Introduction2 Relevant terminologies3 Hazells decomposition- the method4 Study I: Instability in India’s cereal production-

Peter B Hazell5 Study II : Hazell decomposition applied to GR from

arecanut6 Bisaliah’s output decomposition model7 Study I: Application of Bisaliah’s decomposition

model 8 Conclusion9 Reference

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Introduction

• Decomposition is the act of splitting a time series or other system into its constituent parts.

• Most commonly used methods of decomposition are Hazell’s decomposition and Bisaliah’s decomposition.

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Terminologies

• Mean: • Variance:

• Coefficient of variation:• Technical change:

• Neutral technical change:• Non neutral technical change:

• Instability:

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Peter, B. R. Hazell in 1982.

Primarily developed to study instability in Indian food grain production.

Instability in production would mean that there will be price fluctuation.

It will cause varying returns to farmers.

Preamble

I. Hazell decomposition model

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To measure instability panel data at farm level is needed which is

unavailable in most cases.

So Hazell developed statistical methodology to analyze instability using

time series data.

Instability is measured as the change in average production and variance

of production between two periods of time.

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The model

• Let Q denote the production, A the area sown, and Y yield per unit area.

• • Where = Mean area

=Mean yield• Similarly Variance can be written as

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1. Decomposition of change in average production E (Q)

-

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Table 1: Sources of change in average production

Sl.No Sources of Change Symbol Component of change

1 Change in mean yield

2 Change in mean area

3 Interaction between

change in mean area and

mean yield

4 Change in area – yield

Covariance

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A1

A2

Y1 Y2

Y

A

A

C

DA+D

B

A+BA+B+D+C

Increase in Yield

Increase in Area Simultaneous Increase in Yield and area

Fig1: Diagrammatic representation of change in mean production

With the assumption that Cov(A,Y)=0

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Variable Base period Terminal period

Change

Area 3 7 4

Yield 4 3 -1

Production 12 21 9

A*Y1=4*4=16 Y*A1=-1*3= -3

A Y=4* -1= -4

P= 16-3-4=9

Hypothetical illustration….

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The pure effect :

The interaction effect

The variability effect

Sl.

No

Source of change Symbol Components of change

1 Change in mean yield

2 Change in mean area

3 Change in yield variance

4 Change in area variance

5 Interaction between changes in mean yield

and mean area

6 Change in area-yield covariance

7 Interaction between changes in mean area and

yield variance

8 Interaction between changes in mean yield

and area variance

9 Interaction between changes in mean area and

yield and changes in area-yield covariance

10 Change in residual

TABLE 2: DECOMPOSITION OF CHANGE IN VARIANCE OF PRODUCTION

Source : Hazell (1982)

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Study I:Instability in Indian Food grain Production- Peter B.R Hazell (1982)

Objective: To decompose Average production and variance of production to its constituent parts taking

value of Ist Period as base.

Data source: Area and yield of major cereal crops were collected for period

1954 to 1977 from DES and Ministry Of Agriculture.

Ist period: 1954 to 1964 II nd period: 1967 to 1977

Results

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Sl.No

Sources of Change Symbol Rice (%)

Wheat (%)

Bajra (%) Barley (%)

Jowar (%)

Maize (%)

Ragi (%) Total cereals

(%)

1 Change in mean yield

47.92 38.05 76.56 1203.89 153.05 13.36 95.87 47.69

2 Change in mean area

44.65 36.62 19.76 -677.73 -35.71 69.50 -5.71 36.52

3Interaction

between change in mean area and

mean yield

2.23 0.53 1.21 -22.92 6.62 2.06 3.58 1.42

4

Change in area – yield Covariance

5.20 24.80 2.47 -203.23 -23.95 15.06 6.26 14.30

Table 3 : Sources of growth in average production of cereals in India

Source: Hazell (1982)

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Sl. No

Source of change

Symbol Rice (%)

Wheat (%)

Bajra (%)

Barley (%)

Jowar (%)

Maize (%)

Ragi (%)

Total cereals (%)

1 Change in mean yield

-0.69 5.20 0.81 15.08 2.71 0.55 1.24 1.43

2 Change in mean area

1.68 15.75 -0.15 -46.59 -3.81 3.92 2.34 8.75

3 Change in yield variance

40.05 1.12 57.98 -7.88 56.79 48.17 58.66 37.20

4 Change in area variance

5.20 6.86 3.09 -76.50 5.28 -7.08 20.44 5.97

Table 4: Sources of instability in cereal production from India

Source: Hazell (1982)

Sl. No

Source of change

Symbol Rice (%)

Wheat (%)

Bajra (%)

Barley (%)

Jowar (%)

Maize (%)

Ragi (%)

Total cereals

(%)5 Interaction

between changes in mean yield and mean area

1.23 -1.65 -0.15 -0.73 -0.19 -0.19 0.13 0.22

6 Change in area-yield covariance 31.89 11.98 18.52 -8.27 36.12 19.13 24.32 31.04

7 Interaction between changes in mean area and yield variance

18.08 10.95 8.99 8.55 6.13 28.47 -9.14 7.34

8 Interaction between changes in mean yield and area variance

2.19 14.29 2.27 52.22 3.87 0.60 5.34 2.92

9 Interaction between changes in mean area and yield and changes in area-yield covariance

13.17 31.63 8.43 2.22 8.02 7.56 0.67 12.30

10 Change in residual -12.79 3.88 0.21 8.91 -14.91 -1.14 -3.99 -7.16

Contd…………..

18

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Summary of findings

The increase in production of cereals is almost equally attributed to yield and area increase.

With improvement of technology yield and consequently production has

increased so the case with instability.

Variance in yield is the major driver of instability

Input responsiveness of new technologies can be a reason for it

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Study II: Decomposition of GR from arecanut: Application of Hazell’s decomposition model.

(Source: Author)

• Hazell’s decomposition can be applied to any time series which is in turn product of two variables.

Production Imputed price.X =GR

Data and methodology

• Period of study: 1995 to 2010• Base period : 1995-2002 • Terminal period: 2003 to 2010

Data source: Production: Directorate of Economics and

Statistics Imputed price: Special Scheme on Cost of

Cultivation of Arecanut in Karnataka

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Preamble

• Since arecanut is a important commercial crop, returns from the crop affects the fortunes of farmer to a greater extent.

• Objective of the exercise is to know the growth scenario of GR from arecanut over the years in two representative major areca growing districts.

• It will facilitate us in knowing constituent sources of change in average gross revenue and its variance.

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Possible scenario in Growth of GR from arecanut

Growth in GR from arecanut with instability

Growth in GR from arecanut with stability

Declining GR from arecanut with instability

Declining GR from arecanut with stability

Ideal scenario

Expected scenario

Unfavourable scenario

Unfavourable scenario

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Results

Particulars

Shimoga D.K

Percentages Percentages

Change in GR -4.10% -18.00%

Change in mean quantity -1086.70 -220.84

Change in mean price 830.12 235.53

Interaction between change in mean quantity

and mean price371.30 93.52

Change in quantity-price Covariance -14.72 -8.21

 Total 100.00 100.00

Table 5: Source of change in average GR from arecanut

Source : (Author)

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ParticularsShimoga D.K

Percentages Percentages

Change in Variance 50.38 -75.00

Change in mean price -66.73 -0.98

change in mean quantity 780.76 9.78

change in P variance -49.12 132.18

Change in Q variance 117.53 -21.01

Interaction change in mean price and change in mean

Quantity 10.32 -4.26

Change in price quantity covariance 68.56 -30.77

Interaction between change in Price and Q variance -66.59 14.03

Interaction between change in Q and Price variance -1172.74 -2.46

Interaction between changes in mean price and

quantity and changes in price-quantity covariance -3.22 5.97

Residual change 481.23 -2.46

Total 100.00 100.00

Table 6: Source of change in variance of GR from arecanut

Source : (Author)

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Summary of findings

• GR from arecanut has declined in terminal period in both districts.

• The major contributor of this decline is price and its interaction with quantity produced.

• Since GR declined, not much importance to be given to changes in variance.

• Variance in Shimoga increased while that of D. K decreased.

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Advantages and limitations of Hazells decomposition model

Advantages

• No assumption on distribution.

• Useful in instability analysis when used in combination with other measures.

• Helpful in identifying drivers of change.

• Can be applied in variety of situations.

Limitations

• Data oriented methodology.• The components of change

in variance are more of statistical entities and are difficult to interpret and draw policy implications.

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II. Output decomposition model-Bisaliah (1977).

• Productivity difference between potential farm and farmer’s field will be attributed to different sources.

• Change in productivity could be better explained by changes in the parameters which define the production process.

• With the advancement of technology the output increases.• But the increase in output cannot be solely attributed to

technological change.

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A B

M

J

K

L

P

Q

RT

Non neutral technical change

Neutral technical change

Increase in output due to higher inputusage

Figure 2: Diagrammatic representation of technical change

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Steps

21

211101aa xxaY 21

221202bb xxbY

321

210ccc dxxcY

)ln(ln)ln(lnln)(ln)()ln(ln 21222111211222111100 xxbxxbxabxabab

12 lnln YY

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Decomposing productivity differentials…

21

211101aa xxaY 21

221202bb xxbY

21211101 lnlnlnln xaxaaY 22212102 lnlnlnln xbxbbY

)lnxalnx(b)lnxalnx(b)lna(lnblnYlnY 2122221111210012

)lnxblnxblnxalnx(b)lnxblnxblnxalnx(b)lna(lnb)/Yln(Y 2122122122221111111111210012

Add and subtract (b1 lnX11)Add and subtract (b2 lnX21)

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12222122211111112100 ln)()ln(lnln)()ln(ln)ln(ln xabxxbxabxxbab

)ln(ln)ln(lnln)(ln)()ln(ln 21222111211222111100 xxbxxbxabxabab

)lnxblnxblnxalnx(b)lnxblnxblnxalnx(b)lna(lnb)/Yln(Y 2122122122221111111111210012

Neutral technical change

Non neutral technical change

Change in output due to higher input use

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Neutral technical change

Non neutral

technical change

Due to higher input use

Ln Y2-Ln Y1

)ln(ln 00 ab

12221111 ln)(ln)( xabxab

)ln(ln)ln(ln 2122211121 xxbxxb

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Socio-Economic Impact of Bt Cotton — A Case Study of Karnataka: V.R. Kiresur and

Manjunath Ichangi(2011)

Purpose of using the tool:

1) To know how much productivity difference is actually due to Bt cotton technology.

2) To know whether the technology change is more of neutral or non neutral.

3) To know the contribution of various inputs in increasing the yield of Bt cotton.

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Production function usedln Y = ln b0 + b1 ln S + b2 ln F + b3 ln C + b4 ln P + b5 ln H + b6 ln

B + b7 ln M + ui

Y = Gross returns (Rs/ha)S = Seed costs (kg/ha)F = Farm yard manure (tonnes/ha)C = Chemical fertilizers (kg/ha)P = Plant protection chemicals (Rs/ha)H = Human labour (human days/ha)B = Bullock labour (pair days/ha)M = Machine time (hours/ha)bj = Regression coefficients (j=0,1,2…,k) (k=7), andui = Error-term (i=1,2,…,n) (n=30)

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Table 7: Results of output decomposition model

Sl. No. Particulars Percent

Total observed difference in output 26.38Sources of output growth

1 Technology component 26.56 a. Neutral component -138.81 b. Non-neutral component 165.372 Input contribution 0.32 a. Seeds 7.39 b. Farm yard manure -0.38 c. Fertilizer -1.43 d. Plant protection chemicals 0.08 e. Human labour -2.48 f. Bullock labour -0.21 g. Machine -2.653 Total estimated difference 26.88

Source: Kiresur & Manjunath (2011)

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Input

Output

MN

P

Q

A B

Diagrammatic representation of results

26.38%

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Summary of findings

• Bt cotton farmers obtained on an average 26.38 percent higher output compared to non Bt cotton growers.

• Contribution of technology in this increase in output is around 26 percent

• Among the components of technological change lion share is of non neutral technical change.

• Contribution of increased use of inputs towards increase in output is negligible.

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Advantages

• Very simple tool.• Actual contribution of

technology towards increase in output can be known.

• The contribution of various inputs towards increasing output can be known.

Disadvantages

• Accuracy of results depends upon production functions used.

• More of positive than prescriptive.

Advantages and limitations of output decomposition model

Conclusion

• Decomposition is an art of splitting a given time series or a system into its constituent parts.

• Very useful in knowing the drivers of change.• Hazell decomposition is data oriented methodology with

less restrictive assumption, used mainly in instability analysis.

• Output decomposition model developed by Bisalaih is used to know contribution of technology in observed yield difference.

• Since this model is based on production function, it cannot be free of assumption on distribution(Parametric).

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REFERENCES

• HAZELL, P. B. R., 1982, Instability in Indian foodgrain production. International Food Policy Research Institute, Research report 30, Washington, D.C.

• KIRESUR, V. R. And MANJUNATH ICHANGI., 2011, Socio economic impact of Bt cotton- a case study in Karnataka. Agricultural Economics Research Review, 24(1): 67-81.

• PRAKASH, T. N. KAMMARDI, 1997, An Evaluatioin of arecanut cooperative marketing system in Karnataka, Ph.D. Thesis (Unpublished), University of Mysore.

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THANK YOU